Madurai Kamraj University (MKU) 2006 M.Sc Physics " 2 - CLASSICAL MECANICS AND STATISTICAL MECHANICS" - Question Paper
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It's For "M.SC IN IN PHYSICS. MAY 2006 examination ques. Papers ", It'a Course in "Madurai Kamaraj University" or %MK University% in Distance Education Mode
The paper Name Is "M.SC PAPER two - CLASSICAL MECANICS AND STATISTICAL MECHANICS"
This ques. Paper is applicable for those who joined on or after MAY 2006 .
5544/MP2 MAY 2006
Paper II CLASSICAL MECHANICS AND STATISTICAL MECHANICS
Time : Three hours Maximum : 100 marks
Answer ALL questions.
All questions carry equal marks.
5544/MP2 MAY 2006
(5 x 20 = 100)
1. (a) (i) State D'Alembert's principle. Deduce Lagrange's equations of motion from D'Alemberts principle.
(ii) Apply Lagranges equations to solve
(1) The Atwood's machine and
(2) Simple pendulum.
Or
(b) (i) State and explain Hamilton's principle. Deduce Lagranges equations from Hamilton's principle.
(ii) Obtain the velocity of a loop rolling down an inclined plane.
2. (a) (i) How do you covert a two body problem into one body probk;n? Obtain expressions for position and time through equation of motion and first integral.
(ii) State and prove Virial theorem.
Or
(b) (i) Write the Euler's theorem on the motion of a Rigid body. Explain the idea of infinitesimal rotation.
(ii) What are Euler's angles? Explain the different rotations of it.
3. (a) (i) Explain the theory of small oscillations. Apply it to solve the linear molecule problem.
(ii) Write an account on normal coordinates.
Or
(b) (i) State and prove the principle of least action.
(ii) Derive the Hamilton's equations from variational principle.
4. (a) (i) Derive the canonical transforrrt$tion
equations. V
c i -
(ii) Explain the canonical invariance of Lagrange bracket.
Or
(b) What are action-angle variables? Solve the Kepler problem based on action-angle variables.
5. (a) Discuss the types of statistics in detail. Derive the Sackur-tetrode equation for a mono atomic ideal gas.
Or
(b) Explain in detail the brownian motion.
3 5544/MP2
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